Risk

Suppose Aladdin has utility function:

U(W) = 8W W 0 (1)

= W^2 W < 0 (2)

Aladdin has just found the genie's lamp and has wished for a bag of gold since he has nothing at the moment but the clothes on his back. He knows the genie may try to trick him so he has assigned a 25% subjective probability the genie will nd a way to take away his clothes which would cost 4 gold to replace. In addition, he has assigned a 50% subjective probability to getting a medium bag of 64 gold, and a 25% probability of getting a large bag of 100 gold.

A. What is the expected value of Aladdin's gamble?

B. What is the expected utility of Aladdin's gamble?

C. What is the variance of expected utility of Aladdin's gamble?

D. If Aladdin had money, what risk premium would he be willing to pay to avoid bearing the risk of his gamble?